The following strip is for the simplest possible flexagon that supports the v-flex.
It requires 9 leaves and 6 pats, so the simplest flexagon is a hexaflexagon.
Click on the thumbnail to get the full sized version.
Cut it out and copy the small numbers onto the back faces.
Fold each of the adjacent pairs of 3's together.
Tape together the two triangle edges with the dashed lines to make a hexagon.

Start with side 1 facing you.
Take the two points with *'s on them and fold them backwards so they touch.
Open up the flexagon from the center to reveal a pyramid with four 3's in it.
Grab each side of the flexagon and slide the two sides along each other as far as you can
(you may need to rotate the flexagon 180 degrees to make this easier).
You should now have a pyramid with two 1's and two 2's on the inside.
Folding together opposite sides of the pyramid in the right way should allow you to open it back up from the other side.
You should now have four 1's and two 3's on one side and four 3's and two 2's on the other.